SOLUTION: I tried this and came up with 5 but I'm not real sure I have the right answer if it is wrong could you pleae show me how to work this out? Solve the equation ln(x+5)-ln(3)=ln(x-3)

Algebra ->  Equations -> SOLUTION: I tried this and came up with 5 but I'm not real sure I have the right answer if it is wrong could you pleae show me how to work this out? Solve the equation ln(x+5)-ln(3)=ln(x-3)      Log On


   



Question 76556: I tried this and came up with 5 but I'm not real sure I have the right answer if it is wrong could you pleae show me how to work this out?
Solve the equation ln(x+5)-ln(3)=ln(x-3)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
ln%28x%2B5%29-ln%283%29+=+ln%28x-3%29 Apply the quotient rule for logarithms to the left side: ln%28M%29-ln%28N%29+=+ln%28M%2FN%29
ln%28%28x%2B5%29%2F3%29+=+ln%28x-3%29 Now, if ln%28A%29+=+ln%28B%29 then A = B, so...
%28x%2B5%29%2F3+=+x-3 Multiply both sides by 3.
x%2B5+=+3x-9 Subtract x from both sides.
5+=+2x-9 Add 9 to both sides.
14+=+2x Divide both sides by 2.
x+=+7
Check: Substitute x = 7 into the original equation.
ln%287%2B5%29-ln%283%29+=+ln%287-3%29
ln%2812%29-ln%283%29+=+ln%284%29 Using your calculator to find the natural logs:
ln%2812%29-ln%283%29+=+2.4849-1.0986 = 1.3863 and...
ln%284%29+=+1.3863